Relic gravitational waves from quintessential inflation

We study relic gravitational waves in the paradigm of quintessential inflation. In this framework, irrespective of the underlying model, inflation is followed by the kinetic regime. Thereafter, the field energy density remains subdominant before the onset of acceleration. We carry out model-independent analysis to obtain the temperature at the end of inflation and the estimate for the upper bound on the Hubble parameter to circumvent the problem due to relic gravitational waves. In this process, we use Planck 2015 data to constrain the inflationary phase. We demonstrate that the required temperature can be produced by the mechanism of instant preheating. The generic feature of the scenario includes the presence of the kinetic regime after inflation, which results in the blue spectrum of gravitational wave background at high frequencies. We discuss the prospects of detection of relic gravitational wave background in the advanced LIGO and LISA space-born gravitational wave missions. Finally, we consider a concrete model to realize the paradigm of quintessential inflation and show that inflationary as well as postinflationary evolution can be successfully described by the inflaton potential, $V(\varphi )\propto \mathrm{Exp}(-\lambda {\varphi }^n/M_{\mathrm{Pl}}^n)(n>1)$, by suitably constraining the parameters of the model.

Figure 1

Figure shows the parameter space of ($g$, $h$), while the shaded region gives the allowed values of the parameters for efficient preheating to occur. We have used $r={10}^{-3}$ to plot this figure.

Figure 2

Spectral energy density of the relic gravitational wave background for different temperatures have been plotted. The blue (dashed) line corresponds to $T_{\mathrm{end}}=6.29\times {10}^{13}\mathrm{GeV}$ obtained using COBE normalization, while the red (long dashed) and green (dotted) lines have been plotted using the model we have considered in Sec. 4 for temperatures $T_{\mathrm{end}}=2.09\times {10}^{13}$ and $2.09\times {10}^{14}\mathrm{GeV}$, respectively. The numerical values of model parameters are taken to be $n=6$, $r={10}^{-3}$ and $\lambda =8.08\times {10}^{-6}$. Also, we have considered $\mathcal{N}=65$ (behavior does not seem to change significantly for the variation of $\mathcal{N}$), where black solid curves represent the expected sensitivity curves of Advanced LIGO and LISA.